symmetric relation

One example of a symmetric relation is "is equal to".

The third is true because orthogonality is a symmetric relation.

Thus, symmetric relations and undirected graphs are combinatorially equivalent objects.

A self-adjoint morphism is a symmetric relation.

In particular, is a symmetric relation:

Social distance between parties (symmetric relation)

A symmetric relation that is also transitive and reflexive is an equivalence relation.

People from small power distance cultures value equal power distributions, symmetric relations, and rewards and sanctions based on performance.

A symmetric association scheme is one in which each relation is a symmetric relation.

It is clear that the relation of parallelism is a symmetric relation and a transitive relation.

A relation equal to its inverse is a symmetric relation (in the language of dagger categories, it is self-adjoint).

A reflexive and symmetric relation is a dependency relation, if finite, and a tolerance relation if infinite.

Network theory concerns itself with the study of graphs as a representation of either symmetric relations or, more generally, of asymmetric relations between discrete objects.

For relations, a symmetric relation is analogous to a commutative operation, in that if a relation R is symmetric, then .

A key class of such problems stems from the fact that, like adjacency in undirected graphs, intersection of sets (or, more precisely, non-disjointness) is a symmetric relation.

However, as the truth of Heinz's theorem and the falsity of the Schoen-Yau conjecture demonstrate, is not a symmetric relation:

Another dichotomy theorem for constraint languages is the Hell-Nesetril theorem, which shows a dichotomy for problems on binary constraints with a single fixed symmetric relation.

De Broglie could be considered the founder of the wave model in 1925, owing to his symmetric relation between momentum and wavelength: the De Broglie equation.

In mathematics, the symmetric closure of a binary relation R on a set X is the smallest symmetric relation on X that contains R.

"Is a blood relative of" is a symmetric relation, because x is a blood relative of y if and only if y is a blood relative of x.

In an undirected graph, the relation over the set of vertices of the graph under which v and w are related if and only if they are adjacent forms a symmetric relation.

However, if a relation is symmetric, then the argument orders do not matter; thus a symmetric relation with any one of these three properties (transitive, right Euclidean, left Euclidean) must have all three.

Conversely, if R is a symmetric relation over a set X, one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges.

Being conjugate is a symmetric relation: if u is conjugate to v, then v is conjugate to u. (Note: This notion of conjugate is not related to the notion of complex conjugate.)

In terms of the homomorphism problem, every such problem is equivalent to the existence of a homomorphism from a relational structure to a given fixed undirected graph (an undirected graph can be regarded as a relational structure with a single binary symmetric relation).